A quick insight into the essential aspect of the probabilistic modeling perspective can be gained by contrasting it with what it is not. The probabilistic approach does not construct statistical models using algebraic relations. In particular, reasoning about how observed and unobserved quantities relate to each other and how their dependencies are induced does not involve specifying structural relationships using algebraic formulas. Instead, all observed and unobserved events that are thought to represent the phenomenon of interest are denoted by random variables and each event is allocated a finite probability of occurring. That is to say, the generative probabilistic modeling approach is Bayesian in spirit [1]}, [2]}, [3]}. In the probabilistic approach, we start with the joint distribution of all observed and unobserved quantities that govern the distribution of the data.
\(p \left(\mathbf {y}, \theta \right)\) 
